Confirmation of $g_{\mathrm{A}}$ quenching using the revised spectrum-shape method for the analysis of the ${}^{113}$Cd $\beta$-decay as measured with the COBRA demonstrator

Abstract

In this article we present an updated spectrum-shape analysis of the ${}^{113}$Cd fourfold forbidden non-unique $\beta$-decay transition in order to address the quenching of the weak axial-vector coupling $g_{\mathrm{A}}$ in low-momentum exchange nuclear processes. The experimental data were collected in a dedicated low-threshold run with the COBRA demonstrator at the LNGS and resulted in 44 individual ${}^{113}$Cd spectra. These data are evaluated in the context of three nuclear model frameworks based on a revised version of the spectrum-shape method and the conserved vector current hypothesis. The novel idea devised in the present work is to fit the value of the small relativistic nuclear matrix element (s-NME) driving the nuclear model calculations, which remained essentially as a free parameter in previous studies. This is done by tuning the nuclear structure calculations and making use of the interplay of $g_{\mathrm{A}}$ and the s-NME such that the experimentally known ${}^{113}$Cd half-life gets reproducible by the different frameworks. In this way, a best fit s-NME value can be derived for each of the considered nuclear models, which finally enters the template calculations used to perform the spectrum-shape analysis for each of the obtained ${}^{113}$Cd spectra. The primary analysis strategy results in significantly quenched values of the axial-vector coupling for all three nuclear models: ${\overline{g}}_{\mathrm{A}}(\text{ISM})=0.907\pm 0.064$, ${\overline{g}}_{\mathrm{A}}(\text{MQPM})=0.993\pm 0.063$ and ${\overline{g}}_{\mathrm{A}}(\text{IBFM-2})=0.828\pm 0.140$. Moreover, with our data-driven approach one of the main shortcomings of the spectrum-shape method has been resolved. This achievement is a milestone in the description of strongly forbidden $\beta$-decays and adds to the indications for the existence of a quenching of $g_{\mathrm{A}}$ in low-momentum exchange nuclear processes.

Comments: 16 pages, 12 figures